What is (\partial)/(\partial y)(x^{y^z}) ?

The answer to (\partial)/(\partial y)(x^{y^z}) is zx^{y^z}y^{z-1}ln(x)

Popular >

(\partial)/(\partial y)(x^{y^z})

\frac{\partial}{\partial y} (x^{y^{z}})

z x^{y^{z}} y^{z - 1} ln (x)

Solution steps

\frac{\partial}{\partial y} (x^{y^{z}})

Treat

x, z

as constants

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{y^{z}} = e^{y^{z} l n (x)}

= \frac{\partial}{\partial y} (e^{y^{z} l n (x)})

Apply the chain rule:

e^{y^{z} l n (x)} \frac{\partial}{\partial y} (y^{z} ln (x))

= e^{y^{z} l n (x)} \frac{\partial}{\partial y} (y^{z} ln (x))

\frac{\partial}{\partial y} (y^{z} ln (x)) = ln (x) z y^{z - 1}

= e^{y^{z} l n (x)} ln (x) z y^{z - 1}

e^{y^{z} l n (x)} = x^{y^{z}}

= z x^{y^{z}} y^{z - 1} ln (x)

\frac{d}{d x} (ln (\frac{2 x + 1}{x ^{2} - 2}))

\frac{\partial}{\partial x} (4 x^{0.5} + 2 x^{0.25})

\int 2 x e^{4 x} d x

y^{^{'}} + 3 (tan (3 x)) y = - 10 cos (3 x)

\int_{0}^{2} \int 1

What is (\partial)/(\partial y)(x^{y^z}) ?
The answer to (\partial)/(\partial y)(x^{y^z}) is zx^{y^z}y^{z-1}ln(x)